Function generator



Nov- 20, 1962 J. A. HERNDoN FUNCTION GENERATOR 3 Sheets-Sheet l FiledOct. 25, 1960 Nov. 20, 1962 Filed Oct. 25, 1960 VOLTAGE AMPLITUDE J. A.HERNDON 3,064,899

FUNCTION GENERATOR 3 Sheets-Sheet 2 360 SHAFT PosmoN (e) //`-ee l l l iI \I kl TlME E j INVENTOR.

JAMES A, HERNDON.

ATTORNEYS.

NOV- 20, 1962 J. A. HERNDON FUNCTION GENERATOR 5 Sheets-Sheet 3 FiledOCt. 25, 1960 United States Patent fifice Bdigg Patented Nov. 20, 19623,064,399 FUNCTEON GENERATOR James A. Herndon, Cincinnati, Ghia,assigner to Aveo Corperation, Cincinnati, (Ehio, a carpet-atten of Deia-Wa'e Enea on. 2s, rasa, ser. Ne. saaie ri claims. (ci. 23s-i97 Thepresent invention relates to function generators, and it provides animproved function generator in which the output, which is the resultantof the combination of a modifiable function having a discontinuity and amodifier or command, is free from limitations imposed by the approach ofthe modifiable function to its discontinuity.

In accordance with the invention there are provided means for generatinga pair of phase-displaced modifiable functions, each having a given timeto go (before reaching a discontinuity at zero amplitude); means forarbitrarily producing a command or modifier having a maximum valuebetween zero and the maximum amplitude differential between theaforesaid phase-displaced functions; means for selecting that one of themodifiable functions which, when combined with the modifier, hassufiicient time to go to produce the desired resultant function; andmeans for applying the selected modifiable function and the modifier toan adder to produce that resultant.

To define the objects of the invention graphically, let an example of aproblem that it solves be stated. The problem here is to produce, at anyinstant, a resultant or output sawtooth wave form having any desiredamplitude between approximately Zero and an arbitrary selected voltageVR. Assuming a fixed slope, the duration of the sawtooth will beentirely determined by its initial starting amplitude. Now, if it beassumed that a modifiable sawtooth wave form having a maximum amplitudeVR can be initiated at a given time, obviously a sawtooth wave formhaving a maximum amplitude of VR-l/zVR or any other arbitrarily selectedmaximum can be produced by applying to an adder the modiable sawtoothand a subtractive modifier or constant voltage. The time to go of theresultant, if the constant is zero, will be full duration of theresultant sawtooth whose initial amplitude is VR. On the other hand, ifthe constant is 1/2VR, then the time to go (to zero value) of theresultant sawtooth will be reduced by one half. The modifying value of1/zVR takes away half the amplitude of the modifiable sawtooth.

The point is that at any predetermined starting instant it is possibleto apply to a sawtooth wave form a modifier which will reduce the timeto go by any desired amount, and it is feasible by such an expedient toproduce a sawtooth wave form (the same slope being assumed here) of suchinitial amplitude that it will reach Zero value (i.e., itsdiscontinuity) in one minute, five minutes, ten minutes, or fifteenminutes, to give arbitrary examples. However, an approach of this kindsuffers from two serious limitations. One of them is that the command tostart the generation of the desired function must correspond in timewith the beginning of the so-called modifiable sawtooth wave form. Theother limitation resides in the fact that the time to go of theresultant sawtooth wave form is limited by the time to go of the singlemodifiable sawtooth that is available to work with. True it is that, byrepeating the modifiable sawtooth, the supposititious system is improvedat least to the extent that the production of a resultant sawtooth canbe commanded at the start of each successive modifiable sawtooth.Although this reflects some improvement, it is not enough.

It is desirable to provide a resultant sawtooth generator which is notpegged to the initiation of a modifiable sawtooth, but which can becommanded at any time and to any degree, whether the modifiable sawtoothis beginning or at any time point in its trace. I-t is further desirableto provide a resultant sawtooth generator which is not susceptible tothe time to go limitation imposed on a single modifiable sawtooth by theapproach of the modifiable sawtooth to its discontinuity.

These considerations and objectives are applicable not only to agenerator the ultimate function of which is to produce a sawtooth, butto any generator which produces its output by a mathematical operationperformed on a modifiable function which approaches a discontinuity.

It has been stated above that, in accordance with the invention, twomodifiable functions are rendered available, and that the modifier iscombined with that one of the modifiable functions which has sufficienttime to go to provide the desired resultant, An important object of thepresent invention, therefore, is to provide a pair of synchronizedfunction generators which produce continuous phase-displaced functionsof a repetitive nature.

Another object of the invention is to provide, in combination with suchsynchronized function generators, means for producing any desiredmodifier, selecting the discontinuous function desired to be modified,and combining the modifier with the selected discontinuous function toproduce the desired resultant function.

Stated in most simple terms, as applied to one specific embodiment, theprimary object of the invention is to provide an arrangement which willgenerate, beginning at any desired instant (called the instant ofcommand), a resultant sawtooth of any desired amplitude or duration. Ifone is scheduling the arrival of a train, notes that it passes areference point at any instant, and desires to reserve a track in thestation for that train for a period of fifteen minutes, the reservationcould be indicated and suitable track-availability-control equipment setup by initiating the generation of a sawtooth function of fifteen inutesduration at the time of observation of the trains passing theobservation point. Similarly, if at another instant an observer notedanother train passing the observation point, and he desired to reserveanother track for such other train for a period of five minutes, thatcould be accomplished by commanding a function generator to generate asawtooth of live minutes duration and using that sawtooth to controlsuitable track-availability equipment. Thus the utility of a devicewhich can, at any arbitrarily selected instant, produce a sawtooth ofany desired magnitude or duration becomes quite apparent.

For a better understanding of the present invention, together with otherand further objects, advantages, and capabilities thereof, reference ismade to the following description of the appended drawings, in which:

FIG. 1 is a circuit schematic, partly in block diagram form, of acomplete resultant function generator in accordance with the invention;

FIG. 2 is a series of curves employed as an aid in describing theoperation of the synchronized linear function generator portion of theinvention; and

FIGS. 3, 5 and 4 are sets of curves exploited in describing theoperations of the entire system when responding to commands forresultant wave forms of short, medium, and long duration, respectively,and furnishing resultant functions as ordered by said commands.

Referring now to FIG. l, the resultant function produced by thisinvention may be represented by the general equation f(t)-f(k)=f(t).

There are disclosed in FIG. 1 a pair of linear potentiometers 15 and 16.The f(l') of the above equation is generated by one of thepotentiometers 15 or 16, depending on which modifiable function-Le.,linear potentiometer output wave form--is continuous over the period ofduration of the desired function. For the output wave forms of FIGS. 3and 5, the f(.t) is generated by potentiometer 16. For the output Waveform of FIG. 4, the f(t) is generated by potentiometer 15. rl`hese twolinear potentiometers 15 and 16 provide offset functions, one of whichwill always be continuous over a particular interval of interest andwill accordingly be selected for further operations. In FIGS. 3 and 5,wave form or modifiable function 2717 is continuous during the period ofinterest. 'in FiG. 4, wave form 26a, 26b is continuous during the periodof interest. The expression f(t) in the aforementioned equation isreferred to as the modifiable function. In the particular embodimentillustrated, it is one of the sawtooth outputs of the potentiometers 15or 16.

The expression f( k) in the above equation is the modifier. It is theamount subtracted from the selected modifiable function, upon therendering of a command, in ordering the production of the desiredresultant function. The expression f(t") represents the resultantfunction; t is the commanded duration of that function. Since f(t") is asawtooth of the same slope as f(z), the magnitude of the modifierdetermines the initial amplitude of the resultant sawtooth and thereforeits duration.

The modifier f(k) represents the output of the potentiometer 56illustrated in FIG. 1, upon the attainment of the position to which itsrotary arm d5 is ordered when a command is introduced into the system(i.e., when the system departs from idling conditions and generates anoutput function). Now, what the specific embodiment of the inventionhere shown does is to take one of these sawtooth wave forms, hereinafterreferred to as a selected modifiable function or wave form, and also themodifier or output of potentiometer 56, at any desired instant (theinstant of command), and to perform such operations with these data asto process the elected modifiable sawtooth and to generate a resultantoutput sawtooth function of any desired amplitude and duration, having`a maximum possible amplitude of VR and a maximum duration equal to thetime of one half turn of shaft 2:1. The command determines the time atwhich the resultant sawtooth will start, together with its initialstarting amplitude and duration. The command is rendered by causing arm65 of potentiometer 56 to move some predetermined amount to supply theingredient f(k The potentiometers and 16 are so operated and theiroutputs so cycled that, at the time of rendering a command, two modiablefunctions or sawtoo-th wave forms are available. The invention featuresswitching arrangements `by which the desired modifiable sawtooth isautomatically selected. The data corresponding to the first two terms ofthe equation discussed above are applied to adder 69, which furnishesthe desired resultant function on output line 70.

Referring now to FIG. 1, attention is first invited to a pair of linearpotentiometers 15 and 16, the function of which is to generate sawtoothwave forms Z6 and 27, respectively (FIG. 2), these wave forms beingphasedisplaced by 180 degrees in space and therefore in time. This pairof linear potentiometers comprises means for generating modifiableoffset wave `form functions. The potentiometers 15 and 16 have rotarycontact arms 17 and 18, respectively, and circularly arranged uniformresistance portions 19 and 20, respectively. The contact arms aresynchronously driven by a common shaft indicated symbolically by thereference numeral .21, at the rate of,` say, one revolution per hour.This rate and all parameters herein mentioned are set forth for purposesof illustration and not of limitation.

The body portions of the potentiometers are connected in parallelbetween a grounded terminal 22 and the positive terminal 23 of a sourceof voltage, the voltage at terminal 23 having a value of -i-2VR.

The rotating arms 17 and 18 are angularly displaced from each other by180 degrees. As they turn clockwise through 360 degrees, arm 17beginning at the high voltage point 24 on resistor 19 and ending at thelow voltage point 25 on that resistor, potentiometer 1S gencrates asawtooth Wave form 26 (FIG. 2), the first half of which is designated bythe reference numeral 26a, land the second hal-f of which is designatedby the reference numeral Zeb. lt will be understood that the use of theexpression wave form 26 is intended to mean the complete wave form madeup of the halves 26a and 26h. Similarly, the expression wave form 27indicates a total wave form made up of halves 27a and 27b. While thepotentiometer 15 is generating the first half 26a of a sawtooth waveform, potentiometer 16 generates the last half Zb of a similar sawtoothwave form. That is because the potentiometers are so synchronized thatarm 18 leads arm 17 by 18C degrees, and reaches the half-Way point onresistor 20 as arm 17, moving clockwise, touches point 24 on resistor19. While potentiometer 15 is generating the last half 26h of its waveform, the potentiometer 16 is generating the first half 27a of a similarsawtooth wave form.

This action is repeated over and over, once for each revolution of shaft21i.e., once per hour. Thus it will be seen that the potentiometers 15and 16 constitute means for generating degrees phase-displaced sawtootliwave forms, each one hour in duration. At Zerodegree position of shaft21, arm 17 touches 24.

One hour is an illustrative figure. The period involved for sawtoothwave forms is at least twice as long as the maximum duration of anyoutput function to be generated by the invention.

During that part of the operation of the invention which will bereferred to as idling the output wave forms of the two potentiometersare alternately switched between a first bus bar 33 and a second bus bar36 by a doublepole, double-throw switch included in a. relay 30. Thedescription now proceeds to the means by which this switching isaccomplished.

Under the conditions illustrated in FlG. l, the sawtooth wave form 26ais available at switch-blade 29 of relay 3i, and the leading wave form27 is available at blade 31, the blades 2.9 and 31 being conductivelyconnected to the central output terminals of potentiometers 15 land 16,respectively.

It will be observed that each sawtooth Wave form in FIG. 2 reaches aZero value, wave form 26 going through zero at the 360-degree positionof shaft 21 (FIG. 2) when rotary arm 17 reaches point 25, and wave 27(specifically 27h) going through zero when rotary arm 18 reaches thel80-degree position of shaft 21 (FIG. 2) at point 32. It should furtherbe observed that, when either of the wave forms 26 or 27 is at zeroValue, the other Wave form is at half maximum value. It will further beseen that the invention makes available at bus bar 36 the wave formwhich has at least half of its maximum value left to go, even though theother wave form is approaching its discontinuity of zero value. One ofthe contributions of the present invention is the fact that it overcomesthe limitations imposed by the discontinuity of a single wave form, bymaking available always at the bus bars the choice of an alternate waveform which is further away from its discontinuity. To illustrate thelast point, if wave form 27b were selected to be used or modified forthe generation of some output function to begin at an instant fifteenminutes before arm 18 reaches point 32 (i.e., at the 90 degree positionof shaft 21 in FIG. 2), that wave form would have only fifteen minutesto go before reaching its discontinuity (i.e., zero value), while waveform 26 would have a substantially longer time to go.

The bus bars 33 and 36 are so arranged that the last halves 27b and 26bof the wave forms are alternately applied to the first bus bar 33, whilethe first halves 26a and 27a of the wave forms are alternately appliedto the second bus bar 36. Accordingly, the first bus bar 33 is providedwith two input contacts 34 and 35, contact 34 being touched by blade 31to encircuit bar 33 with potentiometer 16 when blade 31 is thrown to theupper one of its two positions, and contact 35 being encircuited withpotentiometer by blade 29 when blade 29 is thrown to its lower position.Likewise, bus bar 36 is provided with input contacts 37 and 38 so thatcontact 38 is touched by blade 29 to encircuit bus bar 36 withpotentiometer 15 when blade 29 is thrown in one direction (upwardly),and so that contact 37 is touched by blade 31 to encircuit bus bar 36with potentiometer 16 when blade 31 is thrown to its other (lower)position. The bus bars and the associated double-pole, doublethrowswitch, including blades 29 and 31, are so arranged that bus bar 33 isencircuited with potentiometer 16 during the iirst half hour of rotationof shaft 21, and with potentiometer 15 during the second half hour,whereby the wave forms 27b and 26b successively appear on the rst busbar 33. In other words, there alternately appear on the first bus bar 33the last halves of the wave form outputs of potentiometers 16 and 15.Bus bar 36 is first encircuited with potentiometer 15 for one-half hour,and is then encircuited with potentiometer 16 for the remaining halfhour, whereby wave form 26a appears on the second bus bar 36 forone-half hour, followed by the wave form 27a. Generalizing, therealternately appear on the second bus bar 36 the first halves of the waveform outputs of potentiometers 15 and 16. Again, what is being describednow is the idling condition.

The switching action, whereby the outputs of the po tentiometers and thebus bars are alternately interchanged, is produced by the action of theblades 31 and 29, under the control of relay 30. That relay is providedwith separate coils 47 and 53, one of which acts through appropriateeXpedients indicated by the dashed line 39 to throw the switch blades 29and 31 in one direction, and the other of which actuates expedients 39to cause the switch blades to be thrown in the other direction. In FIG.1, coil 47 is shown as energized, thereby causing the outputs ofpotentiometers 15 and 16 to be applied to bus bars 36 and 33respectively. When, on the other hand, coil 5.3 is energized, the switchblades 29 and 31 are thrown in the opposite direction and the outputs ofthe potentiometers 15 and 16 are connected to bus bars 33 and 36,respectively.

There will now be described the means by which the selection of thecoils 47 and 53 for energization is accomplished. Attention is invitedto a cam 48 which has 180-degree low and high cam surfaces and isrotatably mounted on shaft 21, in such a manner that when cam 48presents in its low cam surface to element 42 (for the first 180 degreesof its rotation), the switch arms 31 and 29 are in the upper positionillustrated in FIG. 1, and that when cam 43 presents its high camsurface, the blades 29 and 31 are thrown to the lower position. Thereference numeral 40 designates one terminal of a power source (at 28volts, direct current, for example). Between source 46 and ground thereare provided separate selectable energizing circuits for the coils 47and 53. A single-pole, double-throw switch comprising blade 41 isactuated by the cam 48 to connect source 46 either to coil 47 through anon-off switch 45, 46, or to coil 53 through on-oif switch 51, 52. Tothat end the singlepole, double-throw switch having cam-actuated blade41 is provided with a contact 43 (for energization of coil 47) and acontact 49 (for energization of coil 53). It follows from the foregoingthat the low surface of cam 48 throws blade 41 in one direction (asshown in FIG. 1), and the high surface of the cam 48 throws the blade 41in the opposite direction so that coil 53 is energized. The descriptionunder way still relates to the idling condition.

The arrangement is such that cam 48 presents its low surface to element42 during the first 180 degrees of rotation of rotary arms 17 and 18,and it presents its high surface to element 42 during the second 180degrees of rotation of arms 17 and 18.

Each of these two energizing circuits for coils 47 and Cil 53 isprovided with on-oif switches so that, when a command is given to thesystem, a starting relay 54, acting through suitable gauging expedients,throws blades 45 and 51 to disconnect both energizing circuits, leavingrelay 30 in whatever condition it is at the time that the command isgiven. That is to say, if the command is given during the first 180degrees of rotation of shaft 21, then the blades 31 and 29 will remainin the upper position illustrated in FIG. 1. On the other hand, if thecommand is given during the second 180 degrees of rotation of shaft 21,then the switch blades 31 and 29 will remain thrown to their lowerposition. The point is that, when the system goes from the idlingcondition into the generation of a resultant output function, inresponse to a command, the interchanging of connections between the busbars and the linear potentiometers stops.

Reference is now made to the step-by-step potentiometer 56 illustratedin PEG. 1. This potentiometer, on command, produces the modifier k. Thispotentiometer comprises a rotary contact arm 65 and a series of fixedcontacts, arranged in ya circular pattern and, say, ninety in number, ofwhich a few are shown and designated by the reference numerals 1, 2, 3,4, 3113, 39, and. 96 (counting clockwise beginning with 1). Thesecontacts are connected to spaced taps on a resistance voltage divider60, and the voltage divider is connected between ground land thenegative terminal of a supply of direct current, the potential at endtap or terminal 57 having a value of -VR. Contact 1 is connected to endtap 57 and is therefore at a potential of li/R. Contact 2 is connectedto the immediately adjacent tap 62, `and the potential at terminal 2 istherefore It will be understood from the foregoing that the voltage atterminal 911, which is connected to the tap 58, is

That is to say, as the rotary arm 65 sweeps through the fixed contacts,beginning with contact 1 and ending with contact 96, the voltage outputon conductor 59 changes in equal steps from a maximum value -VR to aminimum value and the output voltage value drops to zero as arm 65leaves contact 96 and approaches contact 1. The output voltage of thisstep-type potentiometer appears on output conductor 59, electricallyconnected to arm 65. Illustrative ones of the taps on the voltagedivider 69 are given the reference numerals 62, 63, 64, and 66, tap 66being connected to contact 89, tap 64 being connected to contact 88, tap63 being connected to contact 3, and tap 62 being connected to contact2. i

In the description of the operation of potentiometer 56 during idlingconditions, it will first be supposed for purposes of discussion thatthe output of this potentiometer, as its arm 65 sweeps through 360degrees, beginning at contact 1, is a linear sawtooth wave form whichbegins at a value -VR and continues with the usual slope (i.e., the sameslope as functions 26 and 27) until it reaches a value of zero as arm 65leaves contact 9?. Although the potentiometer output in fact is astep-by-step type sawtooth, it can reasonably be assumed to be a linearsawtooth for purposes of the description immediately ahead. Thishypothetical linear sawtooth is illustrated in FIG. 3, and the referencenumeral 67 is applied to it.

The idling condition operations of the potentiometers 15 and 16 andtheir immediately associated circuitry have been described. The idlingcondition of potentiometer 56 is such that the arm 65 moves from contact90 to contact 1 at the precise time that arm 17 of potentiometer 15reaches the midpoint ofaresistor 19;i.e., at'the shaft 21 position of18() degrees, illustrated in FlG. 2. Now arm 65 of potentiometer 56again passes from contact 9d to Contact 1 when arm 17 of potentiometer15 moves from point 25 to point 24 on resistor 19 (FIG. l). In otherwords, the potentiometers 56, 1.5, and 1e are so synchronized that arm65 operates at twice the angular rate of rotation of arms 17 and 1S.Now, assuming the output of potentiometer 56 to be linear, potentiometer56 would produce a sawtooth wave form 67 having a maximum amplitude of-VR during the time that wave form Z7b is on bus bar 33, and it wouldproduce a like sawtooth wave form 68 during the time that wave form Zebis on bus bar 33 (see FIG. 2).

The output of potentiometer 56 is connected through conductor 59 to anadder 69, and the output of the selected bus bar 33 or 36 is connectedto the adder through switch blade 'ifi yand conductor S5. lt will beseen from an examination of FIG. 2 that, during the zero to 180- degreephase of rotation of shaft 21, wave form Z715 is applied frompotentiometer 16 through the elements 33 and 55 to the adder. The actualwave form generated by potentiometer 56, idealized as 67, is likewiseapplied to the adder during this period. form 67 effectively cancels outWave form 2,711, so that the resultant output on line 7i) is ideallyzero. Considering now the lSO-degree to S60-degree phase of the shaft 21rotation, when wave form 26h is present on bus bar 33 and is applied tothe adder together with the actual wave form idealized as 62, again theefect of the opposingfunction produced by the potentiometer 56 iseffectively to cancel out the wave form 26h. More signiiicant still,what the wave forms 67 and 63 do is suppress the appearance of anysubstantial resultant or output sawtooth function on line 7G until thecommand to generate such a function is introduced into the system. Thatis the reason why the invention can start to produce a desired resultantoutput function at any time and of any duration within the limitationsof the system, such duration being determined by the magnitude of thecommand introduced into the system. Since wave forms 67, for example,normally subtract enough away from wave forms 271') at all times duringidling conditions to reduce the resultant output to zero, this zeroprovides a base-line, as it were, for any desired output function. Itwill now be perceived that one of the keys to the production of anydesired output function is to alter the generation of wave form 67 or 68in a predetermined manner. ln HG. 3, for example, the generation of thewave form idealized as 67, and actually normally having steps la, etc.,under idling conditions, is speeded up on command (per 163) so that theoutput of potentiometer 56 becomes a constant value k1, arm 65 beingarrested at k1 output. lt is this value k1 which is subtracted from waveform 27 b to produce wave form vi), beginning substantially at T1.

Idealized wave forms 6'7 and 68 have been discussed so far. Actually,during the idling condition, the step potentiometer 56 producesstep-type sawtooths which only approximate the linear sawtooth waveforms 67 and 63. Essentially, however, the action is such that the sumof the wave form 27h and the step sawtooth idealized as 67, as appliedto adder 69, approximates zero. So, too, the sum of the step-type waveform shown ideally as 63 and 26b approximates zero.

Potentiometer S6 is a step-type device, and its actual output is not alinear trace 6'7 but is a series of ninety steps such as 1a, 2.a, etc.(FGS. 3, 4, and 5), the 1a and 2a designations indicating that arm 65 ison contact 1 and later on contact 2, and so forth. The steps 1a and 2aare greatly exaggerated in duration and size. Because the output ofpotentiometer 56 is in steps, that output and the linear wave form onbus bar 33, as differentially applied to the adder, cause the resultantoutput appearing under idling conditions on line "itl, ideally zero, toapproximate a series of small triangular sawtooth wave In the adder,wave,

forms, to which the reference, numerals 1b, 2b, etc., arci applied (seeFIGS. 3 and 5). Thesesresidual wave forms 4such as 1b and 2b are of nosignificance, can be reduced to as inconsequential values as may bedesired, and therefore will not further bediscussed herein.

While the cooperative action of thek three potentiometers 15, 16, and56, and the bus bars during idling conditions is that of repetitivelygenerating sawtooth wave forms 27h and 26h, repetitively generatingopposed sawtooth wave forms 67 and 68, and combining the two wave formsto produce an over-all output on line 70 which ideally approximateszero, the action of the system upon the introduction of a command isdilferent in several respects. On command, the amplitude of wave form 67or 68 at the instant of command is suddenly decreased by an amountdetermined bythe magnitude of the command. The amount of this suddendecrease in amplitude determines the duration of the generation of thedesired resultant function, because the decrease in amplitude of thevoltage from potentiometer 56 changes the zero output on line 7d by acorresponding amount substantially at the moment a command is introducedinto the system. 1n other words, on command arm 65 of potentiometer S6is suddenly accelerated, displaced by an amount related to thedurationof the desired resultant function, and then quickly arrested.ThatV is, on command potentiometer 56V produces an output voltage whichis combined with one of the modifiable sawtooth wave forms to produce aresultant sawtooth output Wave form havinga magnitude depending'on suchdisplacement. in FiG. 5, the arm 65 is displaced to a point betweencontacts 9i? and 1, beginning at time T2. Resultant 101 is of mediumduration. 1n FiG. 3, the arm d5 is displaced kapproximately to thetitty-ninth contact beyond 1, beginning at time T1, and the generatedresult-ant 10S is short.

Let it be supposed that, at any arbitrary instant hetween zero and theISO-degree position of shaft 21, arm 65 be very rapidly accelerated anddisplaced by a predetermined number of contact steps. Suppose, forexample, that arm 65 is on contact 2 shortly after shaft 21 passes thezero degrees position. Let it be supposed further that arm 65 isimmediately substantially instantaneously displaced clockwise to aposition between contacts il and 1, reducing the output voltage ofpotentiometer e6 to zero. Applying the potentiometer 56 output value ofzero and the output of bus bar 33 to the adder causes to be generatedaresultant function, appearing on line 70, which would be a wave formidentical in shape and amplitude to that portion of wave form 27bbetween the time of command (very shortly after zero degrees) and thel-degree position. This illustrates the man* ner in which the inventioncan be made to start to generate, at any instant, a resultant wave formequal in duration to the remaining duration of wave form 27h (or 26h) atthat instant. In the example just discussed,- k=0. This example is shownin FlG. 5.

Assuming now the same set of facts, except that the command is earlier(when arm 65 is on contact 1) and is of such a nature as suddenly todisplace arm 65 to a position beyond contact 1 and two-thirds of the wayto contact 9d, and immediately stop it. ln that event the resultant ofthe application of the wave form 27b and the output voltage of thepotentiometer 56 to the adder 69 would be the generation of a wave form(such as 16?, FIG. 3) of substantially smaller amplitude and durationthan wave form 27h. Under the conditions now discussed, k1=approximately/sVR (as shown in FG. 3). Thus it will be seen that, by reason of therendering of commands involving the displacement of arm 65 clockwise,the device can be made to generate, at any instant, a sawtooth wave formofany desired duration up to and inclusive of the maximum remainingduration of wave form 2712 at that instant (FIG. 5). Such resultant waveform (such as 16d, FIG. 5) can be of any starting amplitude between zeroand the maximum amplitude of wave form 27b at the time that the commandis given, neglecting in this discussion the time required for arm 65 toaccomplish the required displacement.

It will be noted that, in what has just been said, the remainingduration of 27b at the time of rendering the command limits theamplitude and duration of the wave form proposed to be generated, thelimitation being faced by reason of the fact that the wave form 27b isapproaching its discontinuity or zero value. One of the principalfeatures of the invention resides in the elimination of this limitation.That is to say, it has been shown that, by issuing a command whichreduces the output of the potentiometer to some magnitude between thecontemporaneous value of 27b and zero, there can be produced a resultantsawtooth wave form having any desired duration short of the remainingduration of wave form 27b.

in accordance with the invention, even greater resalts are obtained. Letit be assumed for purposes of discussion that the command givenaccelerates arm 65 beyond contact 9b, bearing in mind that the largerthe duration of the desired sawtooth to be generated by the adder, thelarger the displacement of arm 65 occasioned by a command. Expressingthe matter another way, let us assume that arm 65 is accelerated anddisplaced beyond contact l to contact 2 or some later contact, and thenarrested. Now, in that event, the output of potentiometer 56 wouldattain a value such that, if it were subtracted from 27b, the resultantwould be a sawtooth smaller than the remaining duration of 27b. But whatis desired is a sawtooth larger than the remaining duration of 27b, andtherefore the output of potentiometer 56 is subtracted from, not thewave form 27b, but the wave form 26a, 26h (see FIG. 4). This isaccomplished by a relay 6i which moves switch arm 74 from contact 76 tocontact 30 whenever, following the issuance of a command, arm 65 passesfrom contact 9@ to contact 1 in other words, whenever the issuance of acommand causes the output voltage of the potentiometer to go throughzero and jump to a maximum; alternately expressed, whenever it isdesired that there be produced a wave form greater in duration than theremaining duration of the smaller sawtooth on the bus bar 33.

Stating the matter another way, if one subtracts a quantity from 27b,one can produce a smaller-amplitude wave form (FIG. 3). If one reducesthat quantity and subtracts less from wave form 27b, one can produce alonger wave form (FIG. 5). lf the quantity subtracted reaches zero, onecannot produce any larger resultant wave form from 27b (FIG. 5).However, the invention further teaches that one can space wave form 27bby VR, an amount equal to the maximum subtractable quantity, from agreater amplitude wave form 26a. When the maximum subtractable quantityis taken away from 26a, the resultant is 27b, from which it follows thata wave form having a maximum amplitude equal to VR is the largest waveform function that the illustrative embodiment is capable of producingat any and all instants of command.

In accordance with the invention, the modiable function having thelarger amplitude or time to go is automatically selected if a command isof such magnitude as to cause arm 65 of potentiometer 56 to moveclockwise beyond contact 90 and on to contact 1. The reason for this isthat, when the desired resultant output function (such as 162, FIG. 4)is of longer duration than the smaller-amplitude modifiable function, itcan be produced by the subtraction of the output of potentiometer 56from the larger-amplitude modifiable function. In this manner thelimitations imposed by the approach of the smaller-amplitude function toits discontinuity are overcome.

It will be understood that the invention starts to work on thesmaller-amplitude function (as in FIG. 3). The

larger the resultant output function desire-d, the more arm 65 isdisplaced by a command, and the less is the voltage value subtractedfrom the smaller-amplitude modifiable function; but, when the commandhas such a value that it displaces arm 65 beyond the zero voltageposition (between contacts and l), then the quantity to be subtracted(i.e., k) is large, and the larger-amplitude modifiable function (26a,FIG. 4) is automatically chosen as the minuend. Assuming the choice ofthe larger amplitude function as the minuend, it will be seen that, forstill longer output functions, the arm 65 is displaced more clockwisebeyond Contact 1, so that the subtrahend diminishes, However, aresultant wave form of one-half hours duration is the maximum that canbe commanded at any and all instants. While FIG. 4 indicates that aresultant wave form longer than one-half hour could be commanded attimes between the zero and ISO-degree position of shaft 2li, it isobvious that at the 180-degree position a resultant having a maximumamplitude of VR, and a maximum duration of one-half hour is the largestresultan wave form that can be commanded.

Now, we have shown that during idling conditions the relay 3ft causesconnections between the linear potentiometers l5 and 16 and the bus bars3.3 and 36 to be interchanged every degrees of rotation of shaft 21.When a command is given to the system, control by relay 30 is removedfrom relay 3i); At the instant that a command is rendered, blade 74 ison contact 76, and that blade remains in that position to put Wave form27b or 26h on line 55, dependent on the shaft position of element 21 atthe time that thel command is given, unless the command causes arm 65 ofpotentiometer 56 to move from contact 90 to contact ll, in which eventrelay 61 causes blade 74 to move to contact Si) and to select eitherwave form 26a or 27a. Once the selection of either 26 or 27 occurs, thatwave form will continue to be applied to the adder from bus bar 36(because the cycling action of relay 36 ceases on the issuance of acommand) until the desired resultant wave form has been generated.

Reference is made to FIGS. 3, 4, and 5 in describing how typical outputfunctions are generated. In FIG. 3 a command is given at time T1, andthe arm 65 of potentiometer 56 is displaced clockwise by approximatelyfifty-nine steps, until the output of that potentiometer reaches a valueof k1. This value is subtracted from wave form 27b to generate theresultant sawtooth function indicated by the reference numeral 100. Itwill be seen that the effect of the rendering of the command is to upsetthe normally balanced relationship of wave form 27b and the wave formidealized as 67.

Now consider the conditions illustrated in FIG. 5, in which the command,initiated at time T2, displaces arm 65 by such an amount as to bring theoutput of potentiometer 56 to zero (just beyond contact 90). In thatcase the resultant wave form 191 is generated.. Since the valuesubtracted from the modifiable function 27b is reduced to zero (i.e.,k=0), the resultant wave form 101 has substantially the same initialamplitude as wave form 27b at the instant of command.

Now assume that a wave form larger than and of longer duration than waveform 161 is desired to be initiated at time T2. Note that wave form 162(FIG. 4) is of such long duration that a subtractive operation on Waveform 27b would not provide it, wave form 27b being of insuicientduration. Also note that the command displaces arm 65 beyond the Zerooutput of potentiometer 56 and beyond contact 1, so that the subtrahendreaches a value k2. Under these conditions, as arm 65 touches contact l,modiable wave form 26 is selected, by the operation of the relay 61.Wave form 26, being further from its discontinuity than wave form 27 is,at time T2, provides an adequate minuend for the generation of thedesire-d output function 102. Thus it will be seen that the inventionwill generate an output function of any 1 1 duration up to one-halfhour, beginning at any instant of command.

The curves 103, 194, and 195 in FIGS. 3, 5, and 4, respectively, showthe behavior of the output Voltage of potentiometer 56 under theconditions pertinent to these figures. The vertical steps are greatlyexaggerated in length and minimized in number for purposes ofillustration. While only three steps are shown in 163, for example, thearm of potentiometer 56 would actually have to move approximately fromcontact 1 to contact 61B (59 steps) to be arrested at an output value ofk1. This assumes that the arm 65 is on contact 1 at the instant ofcommand, and it further assumes that k1 is approximately equal to inwhich case thev maximum amplitude of wave form 11)@ would approximateZVR Consider now the events which occur upon the completion of thegeneration of the desired function. When a wave form 101B reaches zerovalue, the start relay 54 is reset to the FIG. 1 position, and thoseportions of the smallerand larger-amplitude modifiable functions whichremain are applied to bus bars 33 and 36, respectively. Arm 65 ofpotentiometer 56 starts its clockwise rotation, beginning atapproximately the fifty-ninth contact away from contact 1 (assumingoperation per FIG. 3), and the wave form outputs of the potentiometers16 and 56 continue to zero value at the lSO-degree position of shaft 21,whereupon the connections between the linear potentiometers 16 and 15and the bus bars 33 and 36 are interchanged, relay 54- having been resetupon the fulfillment of the command so that the circuits to the coils 47and 53 of relay 3d are again set up for energization. Potentiometer 56resumes its idling condition because the command transmitter 82 gives tothe clutch and braking device 96 a reset order which again coordinatesthe angular motions of that potentiometer with the other two po`tentiometers for idling conditions.

The same simple events occur upon the completion of the generation ofresultant output function 101 (FIG. the bus bar switching occurring atthe ISO-degree position of shaft 21 so that, as idling conditions areresumed, wave form 26b is on bus bar 33 and the larger modifiablefunction 27a is on bus bar 36. The step potentiometer 56resumes idlingby passing to contact 1 between contacts 9i? and 1 at the ISO-degreeposition of shaft 21.

Referring now to FIG. 4, idling conditions are resumed at the conclusionof the generation of output function 1621, the step potentiometer arm 65starting from contact 2. At the time output function 1192 is completed,wave form 26b is on bus bar 36. In this case relay 61 is immediatelyde-energized, and simultaneously the switching device 30 is energized toput 26h on bar 33, and blade 74 is encircuited with bar 33 to apply waveform 26]? to the adder. Wave forms 26h and 68 then continue to approachzero at the S60-degree position of shaft 21.

At this point it is in order to describe the means by which a command isgiven to the system. This means comprises thev command transmitter 82and associated elements. The command transmitter causes the followingoperations to be performed:

First, it is coupled by order and reset circuits to start relay 54, sothat, in rendering a command, it causes relay 54 to break the circuitsof coils 417 and 53, thereby to leave the bus bars 33 and 36 in circuitwith the linear potentiometers to which they were connected at themoment of command.

Second, the command transmitter sends pulses of current through a coil98, magetizing a core 99 and causing arm 65 to speed up-i.c., to advanceclockwise by the desired amount, dependent on the magnitude of thecommand. Thearm 65, due to the action of a known prior art expedient121, advances or is displaced `by one Contact for each pulse. Asindicated, the extent of the advance depends upon the magnitude of thecommand-ie., the number of pulses from the transmitter 82.

Third, the command transmitter is coupled by order and reset circuits toa clutch and braking device 96, which causes arm 65 to stop when it hasbeen displaced by the desired commanded amount.

When the desired resultant function has been generated, the commandtransmitter resets the starting relay 54 and the clutch and brakingdevice 96, so that idling conditions are resumed.

It has been pointed out that, if, in obeying a command, arm 65 ofpotentiometer 56 moves to contact 1, relay 61 is energized to change theposition of blade 74-i.e., to move it from contact 76 to contact 80.That is to say, when response to a command moves arm 65 of potentiometer56 through its zero output point and onto its maximum output point,selector means 61, which normally applies the output of bus bar 33 as amodifiable wave form to the adder, then operates to cause to be appliedto the adder the output of the bus bar 36. What is said here is simplythat the largeramplitude modifiable function is selected (FIG. 4) if aresultant wave form of longer duration than the remaining duration (atthe instant of command) of the smaller-amplitude modifiable function isdesired.

Reference is now made to the means by which the relay 61 is energized.An arm 111 of rotary switch 111) is ganged and coordinated with arm 65.Switch is provided with contacts 112 and 113 which correspond inposition to contacts 9i) and 1. When arm 111 attains a position ofcontact with Contact 113, it sets up an energizing circuit via ground,the coil of relay 61, conductor 85, elements 113 and 111, contact 84,blade 83, conductor 114, contacts 78 and 79 of relay 54, and terminal 77of a voltage source. Upon the rendering of the command and the actuationof the start relay 54, contacts 78 and 79 are closed. The issuance of acommand and magnetizing of core 99 closes blade 83 on contact 34, sothat, at the time arm 65 reaches contact 1, arm 111 touches contact 113and causes relay 61 to be energized. Relay 61 is provided with a holdingcircuit comprising blade 94, contact 95, conductor 93, contact 92, blade87, conductor 86, and direct current voltage terminal 40, the operationbeing such that the start relay 54 Closes contacts 87 and 92 on thegiving of a command and breaks those contacts upon the fulfillment ofthe command. Contacts 94 and 95 are kept in contact by the coil of relay61 so long as the contacts 87 and 92 are made.

It Will be understood that the blades 51, 87, and 78 are controlled inunison by the start relay, the conditions represented in FIG. 1 beingidling conditions and the blades being thrown downwardly by the startrelay on command.

The description of the events geometrically expressed by the wave formsin FIGS. 3, 4, and 5 has postulated that a command is introduced intothe system at some instant between the zero-degree position of shaft 21and the IBO-degree position of that shaft-i.e., during the half-hourperiod represented by the first degrees of rotation of shaft 21. It hasbeen shown that at any instant during this period either the wave formZb or the wave form 26a is available for selection as the minuend forthe mathematical operation performed by the invention. The inventionworks in an equally effective manner if a command is given during thehalfhour period between the instant when shaft 21 reaches its l80-degreeposition and its 360-degree position, either of the modifiable functions26b and 27a then being available for Selection as the minuend. Theinvention has the advantage, therefore, that at any and all instantsthere is available for selection a minuend Wave form more remote fromits discontinuity than the maximum duration of any resultant function tobe produced. The invention accomplishes these results with relativelyfew electrical and mechanical components. The true scope of theinvention includes means, in combination, for performing the variousoperations, and novel combinations of such means, and is not limited tothe particular application shown, nor is it restricted to the specificillustrative means for performing such operations as herein described inthe detail requisite to the disclosure of what is presently deemed to-be the preferred embodiment.

The invention includes, inter alia, the method of generating a resultantfunction (such as 106) which comprises the steps of repetitivelygenerating a function (such as 27h), repetitively generating an opposingfunction (such as the wave form idealized as 67), normally combiningTthe two functions (in adder 69) to produce an output approximating zero,disturbing the generation of the opposing function and arresting it atan assigned arbitrary value (such as k1 in 'Fl'G. 3), whereby theresultant function (such as ffii?) becomes a modified form of thefirst-mentioned function.

The invention further provides the combination of a first functiongenerator ,t6 for generating a function 27 having a discontinuity, asecond function generator 15 for generating a second function 26 havinga discontinuity, means 2l for synchronizing said generators so thattheir outputs are phase-displaced, a first bus bar 33, a second bus bar36, and means (including 43 and 3%) for interchangeably connecting thefunction generators to the bus bars whenever either function reaches itsdiscontinuity, whereby there is always made available on one of the busbars a function substantially removed from its discontinuity.

The invention also provides switching mean 61 for selecting either ofthe aforesaid functions, generally referred to as modifiable functions.While this switching means 6l is so arranged that the smaller-amplitudefunction is normally selected, it automatically selects thelarger-amplitude function if the subtrahend (in response to a command)is of such magnitude as to modify the smaller-amplitude function down tozero.

The invention additionally provides means 56 adjustable on command tosubtract from the selected modifiable function any value up to andincluding the instantaneous amplitude of that function. For example, inFG. 3 the step-type potentiometer 56 subtracts the value k1 from thewave form 271;. The means 39 for interchangeably connecting the functiongenerators to the bus bars is associated with a starting relay 54 andswitch contacts which stop, on command, the interchanging action ofrelay 3?. The means adjustable to perform the subtracting operationfurther comprises an adder 69, to which the selected modifiable functionis applied as a mintiend. The potentiometer du is essentially a thirdfunction generator which normally generates an opposing function(idealized as o7 or o3), which is applied to the adder as a subtrahendto reduce the selected function substantially to zero. it has been shownthat the potentiometer 56 is adjustable on command to provide a constantvalue subtraliend.

Viewing the specific embodiment shown in a narrow aspect, it is aresultant function generator comprising, in combination, first linearpotentiometer means td for generating a series of hrst sawtooth waveforms 27a, 2712 of a predetermined slope each beginning with a maximumamplitude having a voltage value of ZVR; second linear potentiometermeans f5 for generating a series of second sawtooth wave forms 26a, 2615of said predetermined slope each beginning with a maximum amplitudehaving a voltage value of ZVR; each of said linear potentiometer meanshaving a rotary Contact arm f7 or i8, the arm 1S of the firstpotentiometer being angularly displaced by 'ifi 18() degrees from thearm Il? of the second; shaft means 21 for driving the contact arms ofsaid linear potentiometers in synchronism; a iirst bus bar 33; a secondbus bar 36; said linear potentiometers having outputs; relay means 3ufor normally switching the outputs of said potentiometers twice perrotation of the shaft means so that the last halves 27b, 261) of thefirst and second wave forms are alternately applied to the first bus bar33, and the first halves Zea, 27a of the second and next succeedingfirst wave forms are alternately applied to the second bus bar 36,thereby making available at the first and second bus bars a choicebetween phase-displaced sawtooth wave forms, one of said wave formshaving an instantaneous amplitude of VR at each instant when theinstantaneous amplitude of the other wave form is zero; a thirdpotentiometer means S6 for generating in steps a third approximatelysawtooth wave form of said predetermined slope with a maximum ampltudehaving a voltage value of VR; said third potentiometer means havingfixed contacts 1 4, etc. for its steps and a rotary contact arm 65;means for normally so synchronizing the last-mentioned arm with therotary arms of Athe linear potentiometers that the instantaneous `valuesof the third sav/tooth wave forrn 67 are normally substantially equal inamplitude to the wave form output of the first bus bar; adder 69; means:39 for applying the output of the third potentiometer to said adder;selector means el normally applying the output of said first bus bar asa modifiable wave form to said adder but operable to apply to the adderthe output of either bus bar as a modifiable wave form; the third ormodifying wave form 67 from the third potentiometer combining in theadder with the modifiable wave form 27h or Zeb on the first bus bar,under normal conditions, to produce a resultant function approximatingzero output; means 54 subject to a command for disabling the relay means30 to leave the bus bars connected to the linear potentiometers theywere encireuited with at the instant of command; means 121i, 9S, 99subject to a command for accelerating the third rotary arm to displaceit by an ordered amount to a position in contact with one of its fixedcontacts and to arrest the third arm thereat; means lli, M3, 35, 77,755, 79, lll, etc. subject to a command for actuating the selector meansto apply to the adder the output of the second bus bar 36 in the eventthat the third rotary arm 65 passes through its own zero-output positionto its maximum output position while being displaced, whereby, in suchevent, the 4output of the linear potentiometer generating thelarger-amplitude sawtooth is combined in the adder 69 with thesubtractive voltage output of the third potentiometer to produce aresultant sawtooth wave form having a duration determined by themagnitude of the cornmand and a starting point determined by the instantof the command; and command means S2 for controlling the threelast-mentioned means.

For purposes of clarity in explanation, it has been assumed that thestep potentiometer S6 generates an ideal wave form 67 and that theoutput of that potentiometer actually falls to zero when arm 65 movesfrom contact 9i) to contact 1. A supposititious zero output pointbetween these two contacts has been assumed for purposes of discussion,and the petty difference between an ideal wave form such as 67 and awave form approximately the same but having ninety steps has beendisregarded for purposes of clarity in explanation. it will be observed,however, that tlie step voltage output of potentiometer 56, under idlingconditions, never actually reaches zero but has a minimum residual valueof this for the reason that the arm 65 does not in actual practiceattain an open-circuit condition between contacts 90 and 1. If thenumber of steps were infinity rather than ninety, then indeed the outputof potentiometer 56 would reach zero, under idling conditions. it willbe seen from an inspection of FiG. 4 that the curve 185 reaches atheoretical value of zero, and then, as arm 65 moves from contact @il to`contact 2, attains a value of k2. in -view of the fact that there areninety discrete steps instead of an infinity of steps, the wave form tlwill not in practice actuall go to zero value, hut its minimum valuewill be Since, by increasing the denominator of this fraction thisresidual value can be made to approach zero, the theoretical zeroassumed for purposes of explanation is believed to be in order and inthe interests of clarity. This comment is directed to the operationunder command conditions or idling conditions.

While there has been shown and described what is at present consideredto be the preferred embodiment of the present invention, in detail,further definition of the word command is in order. rfhe word commandindicates the amount by which the arm 5S is suddenly displaced when thesystem is actuated to produce an output function. The duration of theresultant output function depends only on the magnitude of the commandand is independent of the instant of command. This is true because thecommand causes a disturbance of a normally approximately balancedrelationship-as, for example, that between wave forms o7' and 27h inFIG. 3. This substantially balanced relationship prevails until acommand is rendered, and the magnitude of the command, as illustrated inPEG. 3, is the amount of the sudden displacement of arm 65, or thedifference between the k1 voltage output position (of potentiometer S6)which the ar .i suddenly assumes and the contact position on which itwas at the time the command was rendered.

1t will be understood by those skilled in the art that various changesand modications may be made in the preferred embodiment withoutdeparting from the true scope of the invention as defined in theappended claims. For example, it is known that the various modifiablefunctions here involved can be generated mechanically, hydraulically, orelectrically. It is also know that algebraic combination or subtractionlikewise can be accomplished electrically, mechanically, orhydraulically. The same is true with reference to the generation of thesubtrahend. Therefore, it is not intended, in the presentation of thepreferred embodiment above described in detail, to limit the inventionto the particular electrical and mechanical means chosen as the functiongenerators and operators. It is intended to cover a proper range ofequivalents.

I claim:

1. The combination of a first function generator for generating afunction having a discontinuity, a second function generator forgenerating a second and similar function having a discontinuity, meansfor synchronizing said generators so that their outputs arephasedisplaced by an amount equal to half the duration of eitherfunction, a first terminal, a second terminal, and means forinterchangeably connecting the function generators to the terminalswhenever either function reaches its discontinuity, whereby there isalways made available a choice between functions, the last-mentionedmeans comprising a timer having two alternating states each of which isequal in duration to half the duration of either function, and a switchcontrolled by the timer for interchanging the connections between thefunction generators and the terminals whenever the timer changes itsstate.

2. The combination of first and second sawtooth generatingpotentiometers, each having a rotary arm, the arm of the firstpotentiometer leading the arm of the second potentiometer by 180degrees, first and second bus bars, and double-pole, double-throwencircuiting means for connecting the outputs of the first and secondpotentiometers to the rst and second bus bars, respectively, during thefirst,l80. degrees of angular movement of said arms, starting with thesecond potentiometer at its maximum output, and for connecting thesecond and first potentiometers to the first and second bus bars,respectively, during the second degrees of angular movement of saidarms, means for driving said arms in synchronism, and means including acam synchronized with the driving means for actuating the double-throwencircuiting means.

3. The combination of claim 2 and a step-type potentiometer having aplurality of fixed contacts arranged in a circular pattern together witha rotary arm, a tapped voltage divider connected to said fixed contactsin a sequence such that the step-type potentiometer generateseffectively a stepped sawtooth wave form, the last-mentioned rotary armbeing operated at twice the angular rate of the rotary arms of the firstand second potentiometers and so coordinated therewith that thestep-potentiometer output of VR is at a maximum when the sawtoothappearing on the first bus bar is at its maximum of VR, and means fordifferentially combining the sawtooth appearing on the first bus bar andthe step-sawtooth output of said step-type potentiometer.

4. The combination of a first function generator for generating afunction having a discontinuity, a second function generator forgenerating a second function having a discontinuity, means forsynchronizing said generators so that their outputs are phase-displaced,a first terminal, a second terminal, means for interchangeablyconnecting the function generators to the terminals whenever eitherfunction reaches its discontinuity, vwhereby there is always madeavailable a choice between functions, selector switching means forselecting either of said functions as a modifiable function, and meansadjustable on command to subtract from the selected function any valueup to and including its instantaneous amplitude at the instant ofcommand, but not to exceed half of the maximum amplitude of saidfunction.

5. The combination in accordance with claim 4, and means for stopping,on command, the means interchangeably connecting the generators to thebus bars.

6. The combination in accordance with claim 5 in which the selectorswitching means normally selects the smaller-amplitude one of saidfunctions but operates on command to select the larger-amplitudefunction as a modifiable function whenever said value exceeds theinstantaneous amplitude of the smaller-amplitude function.

7. The combination in accordance with claim 6 in which the meansadjustable to perform a subtracting operation includes an adder coupledto the selector switching means, to which adder the selected modifiablefunction is applied as a minuend, and further includes a third functiongenerator coupled to said adder, which third function generator normallygenerates an opposing function applied to the adder as a subtrahend toreduce the selected function substantially to zero, but which includesan arm adjustable on command to provide a constant-value subtrahend.

8. The combination in accordance with claim 7 in which the first andsecond function generators generate sawtooth wave forms of identicalslope.

9. The combination in accordance with claim 8 in which the thirdfunction generator is a step-type potentiometer which includes said armand generates a steptype sawtooth.

10. The combination of a rst function generator for generating afunction ZVR-s (t9-180 degrees), a second function generator forgenerating the function ZVR-s (6), first and second bus bars, switchmeans for interchangeably connecting the first and second generators tothe bus bars every 180 degrees, so that the last half of each functionis applied to the first bus bar and the 17 first half of each functionis applied to the second bus bar, a third generator for generating astep function having half the duration and maximum amplitude of the twoaforementioned functions, means for differentially combining the stepfunction and the function applied to a selected one of said bus bars,wherein ZVR is the maximum amplitude in voltage of each of therst-mentioned functions, n is the maximum number of steps in the stepfunction, m is the number of steps through which the step function haspassed at any instant, and s is the slope; means for stopping, oncommand, the interchangeably connecting means; means for instantaneouslyaccelerating the third generator on command and arresting it at any stephaving a constant output value such as to provide a resultant outputsawtooth of desired duration; and selector means for selecting theoutput of either the first or the second function generator as amodifiable function, said selector means normally selecting thesmaller-amplitude one of said functions but operable on command toselect the larger-amplitude one whenever said constant value exceeds theinstantaneous amplitude of the smaller-amplitude function.

11. Means for repetitively generating a rst sawtooth Wave-form functionof 360 degrees duration, means for repetitively generating a like secondsawtooth waveform function of 360 degrees duration lbut phase-displacedfrom the first function by 18() degrees, means for repetitivelygenerating a third similar sawtooth function of half the amplitude andtwice the frequency of the aforementioned two functions, first andsecond terminals, means for alternately coupling the first twogenerating means to the first terminal normally to present the lasthalves of said two functions at said first terminal, said meansalternately coupling the first two generating means to the secondterminal normally to present the first halves of said two functions atsaid second terminal, means for disturbing the generating of the thirdfunction and arresting it on command at some arbitrary value, means forstopping the alternate action of the coupling means on command, meansnormally connected to said first terminal for subtracting that arbitraryvalue from the wave form on the first terminal if that Wave form is atleast equal in amplitude to said arbitrary value at the instant ofcommand, and means responsive to command for switching the connection ofthe subtracting means to said second terminal in the event that theamplitude of the wave form on the first terminal is less than saidarbitrary value at the instant of command.

References Cited in the file of this patent UNITED STATES PATENTS UNITEDSTATES PATENT OEETCE CEBTEFICATE 0F C0 RECH November 2Ou 1962 James A7Herndon lt is hereby certified that error appears in the above numberedpatent requiring correction and that Jche said Letters Patent shouldread as corrected below..

Column l line ll before "full" insert m the mg column 5 line L8v strikeout; "i1/11"; column ll line '50 strike out to Contact 1"; line 741 for"magetzing" read magnetizing w; column l3 line 37V for "mean" read means-f-D Signed and sealed this 28th day of May 1963,

(SEAL) Attest DAVID L. LADD Commissioner of Patents ERNEST W. SWIDER Aesting @fficer

